From Poincare to affine invariance: How does the Dirac equation generalize?

A generalization of the Dirac equation to the case of affine symmetry, with SL(4,R) replacing SO(1,3), is considered. A detailed analysis of a Dirac-type Poincare-covariant equation for any spin j is carried out, and the related general interlocking scheme fulfilling all physical requirements is established. Embedding of the corresponding Lorentz fields into infinite-component SL(4,R) fermionic fields, the constraints on the SL(4,R) vector-operator generalizing Dirac's gamma matrices, as well as the minimal coupling to (Metric-)Affine gravity are studied. Finally, a symmetry breaking scenario for SA(4,R) is presented which preserves the Poincare symmetry.Comment: 34 pages, LaTeX2e, 8 figures, revised introduction, typos correcte

Spectra of Discrete Schr\"odinger Operators with Primitive Invertible Substitution Potentials

We study the spectral properties of discrete Schr\"odinger operators with potentials given by primitive invertible substitution sequences (or by Sturmian sequences whose rotation angle has an eventually periodic continued fraction expansion, a strictly larger class than primitive invertible substitution sequences). It is known that operators from this family have spectra which are Cantor sets of zero Lebesgue measure. We show that the Hausdorff dimension of this set tends to $1$ as coupling constant $\lambda$ tends to $0$. Moreover, we also show that at small coupling constant, all gaps allowed by the gap labeling theorem are open and furthermore open linearly with respect to $\lambda$. Additionally, we show that, in the small coupling regime, the density of states measure for an operator in this family is exact dimensional. The dimension of the density of states measure is strictly smaller than the Hausdorff dimension of the spectrum and tends to $1$ as $\lambda$ tends to $0$

Gamma-widths, lifetimes and fluctuations in the nuclear quasi-continuum

Statistical $\gamma$-decay from highly excited states is determined by the nuclear level density (NLD) and the $\gamma$-ray strength function ($\gamma$SF). These average quantities have been measured for several nuclei using the Oslo method. For the first time, we exploit the NLD and $\gamma$SF to evaluate the $\gamma$-width in the energy region below the neutron binding energy, often called the quasi-continuum region. The lifetimes of states in the quasi-continuum are important benchmarks for a theoretical description of nuclear structure and dynamics at high temperature. The lifetimes may also have impact on reaction rates for the rapid neutron-capture process, now demonstrated to take place in neutron star mergers.Comment: CGS16, Shanghai 2017, Proceedings, 5 pages, 3 figure

Using cascading Bloom filters to improve the memory usage for de Brujin graphs

De Brujin graphs are widely used in bioinformatics for processing next-generation sequencing data. Due to a very large size of NGS datasets, it is essential to represent de Bruijn graphs compactly, and several approaches to this problem have been proposed recently. In this work, we show how to reduce the memory required by the algorithm of [3] that represents de Brujin graphs using Bloom filters. Our method requires 30% to 40% less memory with respect to the method of [3], with insignificant impact to construction time. At the same time, our experiments showed a better query time compared to [3]. This is, to our knowledge, the best practical representation for de Bruijn graphs.Comment: 12 pages, submitte

Lyapunov exponent and natural invariant density determination of chaotic maps: An iterative maximum entropy ansatz

We apply the maximum entropy principle to construct the natural invariant density and Lyapunov exponent of one-dimensional chaotic maps. Using a novel function reconstruction technique that is based on the solution of Hausdorff moment problem via maximizing Shannon entropy, we estimate the invariant density and the Lyapunov exponent of nonlinear maps in one-dimension from a knowledge of finite number of moments. The accuracy and the stability of the algorithm are illustrated by comparing our results to a number of nonlinear maps for which the exact analytical results are available. Furthermore, we also consider a very complex example for which no exact analytical result for invariant density is available. A comparison of our results to those available in the literature is also discussed.Comment: 16 pages including 6 figure

The American Psychiatric Association’s Guideline for Major Depressive Disorder: A Commentary

The American Psychiatric Association (APA) published a new guideline for Major Depressive Disorder (MDD) which will undoubtedly be used by many practitioners to guide clinical decision-making. In fact, it is non-psychiatrist clinicians who prescribe the majority of antidepressants (AD). We review the APA’s most recent guideline on MDD and report on our observations

The XMM-Newton view of the Crab

Aims. We discuss the current X-ray view of the Crab Nebula and Pulsar, summarising our analysis of observations of the source with the EPIC-pn camera on board the XMM-Newton observatory. Different modes of EPIC-pn were combined in order to yield a complete scenario of the spectral properties of the Crab resolved in space and time (pulse phase). In addition we give a description of the special EPIC-pn Burst mode and guidance for data reduction in that mode. Methods. We analysed spectra for the nebula and pulsar separately in the 0.6−12.0 keV energy band. All data were processed with the SAS 6.0.0 XMM-Newton Scientific Analysis System package; models were fitted to the data with XSPEC 11. The high time resolution of EPIC-pn in its Burst mode (7 μs) was used for a phase resolved analysis of the pulsar spectrum, after determination of the period with epoch folding techniques. Data from the SmallWindow mode were processed and corrected for pile-up allowing for spectroscopy simultaneously resolved in space and time. Results. The spatial variation of the spectrum over the entire region of the Crab shows a gradual spectral softening from the inner pulsar region to the outer nebula region with a variation in photon index, Γ, from 2.0 to 2.4. Pulse phase resolved spectroscopy of the Crab Pulsar reveals a phase dependent modulation of the photon index in form of a significant hardening of the spectrum in the inter-peak phase from Γ = 1.7 during the pulse peak to Γ = 1.5